Related papers: Self-similar imploding relativistic shock waves
It is known that a nonlinear Schr\"odinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such…
We study a collapsing system attracted by a spherically symmetric gravitational source, with an increasing mass, that generates back-reaction effects that are the source of space-time waves. As an example, we consider an exponential…
Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
The Naval Research Laboratory "Mag Noh problem", described in this paper, is a self-similar magnetized implosion flow, which contains a fast MHD outward propagating shock of constant velocity. We generalize the classic Noh (1983) problem to…
We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These…
We report on numerical simulations of critical phenomena near the threshold of black hole formation in the collapse of axisymmetric gravitational waves in vacuum. We discuss several new features of our numerical treatment, and then compare…
The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity…
The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an…
Although local existence of multidimensional shock waves has been established in some fundamental references, there are few results on the global existence of those waves except the ones for the unsteady potential flow equations in…
We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt 0.036$, it has been known that there exists a general relativistic counterpart of the…
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is…
A pair of simple wave equations is presented for the symmetric gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled, and the other has a source term given by the solution of the first…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
Building upon the pioneering work [Merle, Rapha\"el, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413, 2022] we construct exact, smooth self-similar imploding…
We consider the Cauchy problem for the wave equation in a general class of spherically symmetric black hole geometries. Under certain mild conditions on the far-field decay and the singularity, we show that there is a unique globally smooth…
We perform fully nonlinear numerical simulations to study aspherical deformations of the critical self-similar solution in the gravitational collapse of ultra-relativistic fluids. Adopting a perturbative calculation, Gundlach predicted that…
We study the gravitational shock wave generated by a massless high energy particle in the context of higher order gravities of the form $F(R,R_{\mu \nu}R^{\mu \nu},R_{\mu \nu \alpha \beta}R^{\mu \nu \alpha \beta})$. In the case of $F(R)$…
The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative…
Propagation of the strong shock in the flat expanding Friedman universe is investigated using methods of dimension and similarity. Exact analytic solution of self-similar equations is obtained, determining dependences of the radius and…